In motors of this type, the pistons cause the rotation of the motor crankshaft which is supported in bearings located in housings set in the frame or integral with the frame, by acting on the eccentric part of the shaft. The cylinders in which the pistons slide may be integral with the frame or hinged to it. In some known versions of rotary motors of variable cylinder capacity, the variation of the cylinder capacity is obtained by varying the eccentricity of the crankshaft by means of hydraulic jacks controlled by valves which are located in the shaft and are supplied through a rotating collector formed by making use of the connection between a pin of the shaft and the frame, with the aid of seals for the rotating shaft. These variable-capacity rotary hydraulic motors have various disadvantages: for example, they do not have a cylinder capacity which is stable at all the values within the range of variation; they have to be dismantled and disconnected from the controlled parts for the maintenance of the aforesaid valves and seals for the rotating shaft (which are subject to much stress); and they are subject to considerable energy losses due to friction and leakage. All the above factors combine to make such motors deficient in performance, reliability and efficiency, which considerably limits their application.